The article you linked to doesn't show this. The pie graph at the end has a big green chunk which refers to, "Remaining health care spending". It doesn't say this only pertains to patient care. Also the chart is about spending higher than expected given our wealth.

I didn't find a place in the article that talked about administrative costs (i.e. salaries, bonuses, profits) that go to insurers.

Insured middle classes competing directly with the super-rich over a limited pool of medical professionals is probably the biggest culprit.

I don't believe that is the case. Otherwise, we would see a shortage of care provided. Since everyone gets care, the competition with the super rich- if any- is vote driving prices

And you don't think you see a shortage of care provided?

[edit] And hang on a second. You say if any? Really? You think there is no competition for resources?